A connection between viscous profiles and singular ODEs

We deal with the viscous profiles for a class of mixed hyperbolic-parabolic systems. We focus, in particular, on the case of the compressible Navier Stokes equation in one space variable written in Eulerian coordinates. We describe the link between these profiles and a singular ordinary differential equation in the form $$dV / dt = F(V) / z (V) .$$ Here $V \in R^d$ and the function F takes values into $R^d$ and is smooth. The real valued function z is as well regular: the equation is singular in the sense that z (V) can attain the value 0.Comment: 6 pages, minor change

V4743 Sgr, a magnetic nova?

Two XMM Newton observations of Nova V4743 Sgr (Nova Sgr 2002) were performed shortly after it returned to quiescence, 2 and 3.5 years after the explosion. The X-ray light curves revealed a modulation with a frequency of ~0.75 mHz, indicating that V4743 Sgr is most probably an intermediate polar (IP). The X-ray spectra have characteristics in common with known IPs, with a hard thermal plasma component that can be fitted only assuming a partially covering absorber. In 2004 the X-ray spectrum had also a supersoft blackbody-like component, whose temperature was close to that of the white dwarf (WD) in the supersoft X-ray phase following the outburst, but with flux by at least two orders of magnitude lower. In quiescent IPs, a soft X-ray flux component originates at times in the polar regions irradiated by an accretion column, but the supersoft component of V4743 Sgr disappeared in 2006, indicating a possible origin different from accretion. We suggest that it may have been due to an atmospheric temperature gradient on the WD surface, or to continuing localized thermonuclear burning at the bottom of the envelope, before complete turn-off. An optical spectrum obtained with SALT 11.5 years after the outburst showed a prominent He II 4686A line and the Bowen blend, which reveal a very hot region, but with peak temperature shifted to the ultraviolet (UV) range. V4743 Sgr is the third post-outburst nova and IP candidate showing a low-luminosity supersoft component in the X-ray flux a few years after the outburst.Comment: 9 pages, 5 figures, accepted to MNRA

Characteristic Boundary Layers for Mixed Hyperbolic-Parabolic Systems in One Space Dimension and Applications to the Navier-Stokes and MHD Equations

We provide a detailed analysis of the boundary layers for mixed hyperbolic\u2010parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so\u2010called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so\u2010called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic\u2010parabolic system and for the hyperbolic system obtained by neglecting the second\u2010order terms. Our analysis applies in particular to the compressible Navier\u2010Stokes and MHD equations in Eulerian coordinates, with both positive and null electrical resistivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to nonconservative systems

The boundary Riemann solver coming from the real vanishing viscosity approximation

We study a family of initial boundary value problems associated to mixed hyperbolic-parabolic systems: v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x = \epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx} The conservative case is, in particular, included in the previous formulation. We suppose that the solutions $v^{\epsilon}$ to these problems converge to a unique limit. Also, it is assumed smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $A$ can be $0$. Second, we take into account the possibility that $B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.Comment: 84 pages, 6 figures. Text changes in Sections 1 and 3.2.3. Added Section 3.1.2. Minor changes in other section

Promoting post-stroke recovery through focal or whole body vibration: criticisms and prospects from a narrative review

Objective: Several focal muscle vibration (fMV) and whole body vibration (WBV) protocols have been designed to promote brain reorganization processes in patients with stroke. However, whether fMV and WBV should be considered helpful tools to promote post-stroke recovery remains still largely unclear. Methods: We here achieve a comprehensive review of the application of fMV and WBV to promote brain reorganization processes in patients with stroke. By first discussing the putative physiological basis of fMV and WBV and then examining previous observations achieved in recent randomized controlled trials (RCT) in patients with stroke, we critically discuss possible strength and limitations of the currently available data. Results: We provide the first systematic assessment of fMV studies demonstrating some improvement in upper and lower limb functions, in patients with chronic stroke. We also confirm and expand previous considerations about the rather limited rationale for the application of current WBV protocols in patients with chronic stroke. Conclusion: Based on available information, we propose new recommendations for optimal stimulation parameters and strategies for recruitment of specific stroke populations that would more likely benefit from future fMV or WBV application, in terms of speed and amount of post-stroke functional recovery

Low-Cost Uas Photogrammetry for Road Infrastructures' Inspection

Abstract. All over the world, road infrastructures are getting closer to their life cycle and need to be constantly inspected: a consistent number of bridges are structurally deficient, and the risk of collapse can no longer be excluded. In contrast with the past, the interest in structure durability has recently grown rapidly. In order to make bridges durable, it is necessary to carry out ordinary maintenance, preceded by inspection activities, which can be traditionally divided in two categories: destructive and non-destructive (NDT). All the NDT inspections (visual, IR thermography, GPR) can be conducted by using UAS (Unmanned Aerial Systems), a technology that makes bridges inspections quicker, cheaper, objective and repeatable. This study presents the visual inspection and survey of two bridges by using a UAS DJI Mavic 2 Pro, equipped with a 20Mpixel Hasselblad camera that records 60fps 4K video and a 10bit radiometric resolution. Starting from the acquired data, a 3D model of each structure was built by using Structure from Motion (SfM) principles and software. To validate the two models, each of them characterized by a centimetric accuracy, the UAS camera generated cloud of points and was co-registered with the point cloud of a terrestrial laser-scanner using Ground Control Points (GCPs). To make this, CloudCompare comparison software was used; the plugin M3C2 automatically calculates the distance between the points of two compared clouds. Finally, some general rules concerning the UAS main characteristics for inspection of bridges and software for data processing are proposed